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~\vspace{8cm}
\begin{center}
    \textbf{\Large Capstone Engineering, Fall 2008: Arcata Brackish Marsh Project  \\ Individual Writing Component}
    {\bf\\ Jason M. Roberts \\}
    \today
\end{center}
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\onehalfspacing
\section{Introduction}
The City of Arcata has requested action by the HSU Capstone
Engineering Team regarding the integration of a new Brackish Marsh
into the city's wastewater treatment process. The Brackish Marsh,
constructed in the summer of 2008, is part of a larger McDaniel
Slough restoration project focusing on the creation of diverse
habitat for birds and fish. Freshwater inflow from the treatment
plant and saltwater flow from Humboldt Bay will mix to create the
desired brackish conditions. A tidal model provided by the National
Oceanic \& Atmospheric Administration's (NOAA) will predict tidal
elevation in McDaniel Slough. The objective of this project is
twofold: (1) to investigate the hydraulic feasibility of connecting
the Brackish Marsh in series with the existing treatment system
while maintaining a single point of discharge, and (2) to produce an
operational tool for examining "what-if" scenarios during extreme
inflow events. Several possible flow scenarios are investigated
based on the possible outcomes of ongoing discharge permit
negotiations. This paper outlines the results of the feasibility
study, including: (1) the existing and proposed conditions of the
marsh system, (2) a review of relevant literature for hydraulic
model development, inflow forecasting, and tide gate modeling, (3)
application and results of the marsh system model, and (4) a
discussion and analysis of feasible Brackish Marsh integration
scenarios.

\section{Background \& Literature Review}
\subsection{Arcata Community and Wastewater Treatment Facility Profile}
The City of Arcata in is located northwestern California on
the north rim of Humboldt Bay (Figure \ref{fig:vicinity}).
\begin{figure}[!h]
  \centering
     \subfigure[The city of Arcata's location in Northern California.]
     {\includegraphics[scale=.35]{figs/Norcal.pdf}}
     \centering
     \subfigure[The location of Arcata's wastewater treatment plant.]
     {\includegraphics[scale=.35]{figs/Overhead.pdf}}
  \caption{The location of Arcata, CA, and the city's wastewater treatment facility \citep{Roberts2008}.}
  \label{fig:vicinity}
\end{figure}
The Arcata Wastewater Treatment Plant (AWWTF) is an integrated
wetland treatment system and wildlife sanctuary, serving a
population of approximately 15,000 during the academic year. The
facility was designed and built in 1984 to treat an average
wastewater flow of 2.3 MGD. The treatment process consists of a
conventional primary treatment train with secondary and tertiary
treatment provided by the oxidation ponds, treatment marshes, and
enhancement marshes \citep{CH2MHill}. A comprehensive flow diagram
of the treatment system is located in Appendix A. Excessive inflow
and infiltration of the sewer collection system during the winter
months can cause spikes in plant inflow that lead to discharge
violations, a problem this project hopes to alleviate.


\subsection{A Brief History of the AWWTF}
The site of the current WWTF was originally covered by brackish
wetlands and used extensively by native American populations. Early
development led to Humboldt Bay dike construction and the filling in
of the brackish wetlands for solid waste disposal. In 1940, the
AWWTF was constructed to provide primary treatment only. Prior to
1940, waste was simply discharged to the bay via a 400 ft pipe. In
1958, 55 acres of oxidation ponds were added to the treatment
scheme, followed by the controversial addition of the treatment and
enhancement marshes in 1977 \citep{Points2008}.

\subsection{AWWTF Discharge Permit \& Associated Violations}
The current permit of waste discharge (NPDES Permit No. CA0022713)
was issued in June of 2004 and will expire in June of 2009. The
permit grants the use of two discharge points: Butcher Slough
(outfall No. 001), and the Enhancement Marshes (outfall No. 002) in
the Arcata Marsh and Wildlife Sanctuary. The Permit imposes
pollutant discharge regulations at each of the permitted discharge
points (Table \ref{tab:001}, Table \ref{tab:002}), and strictly
prohibits any unregulated discharges into Humboldt Bay.
\begin{table}[!h]
   \centering
   \caption{Discharge limitations at Outfall No. 001 \citep{CRWQCB2004}.}
   \begin{tabular}{ccccc}
      \toprule
        & Units & Monthly Average & Weekly Average & Daily Maximum \\
      \midrule
      BOD$_5$           & mg/L      & 30                  & 45 & 60   \\
      Suspended Solids  & mg/L      & 30                  & 45 & 60   \\
      Settleable Solids & mL/L      & 0.1                 & -  & 0.2  \\
      Fecal Coliform    & MPN/100mL & 14                  & -  & 43   \\
      pH                & Standard  & $>$ 6.0 and $<$ 9.0 &    &      \\
      Copper            & $\mu$g/L  & 2.8                 & -  & 5.7  \\
      Zinc              & $\mu$g/L  & 47                  & -  & 95   \\
      Cyanide           & $\mu$g/L  & 0.5                 & -  & 1.0  \\
      2,3,7,8-TCDD TEQ  & pg/L      & 0.014               & -  & 0.028\\
      \bottomrule
   \end{tabular}\label{tab:001}
\end{table}
\begin{table}[!htbp]
   \centering
   \caption{Discharge limitations at Outfall No. 002 \citep{CRWQCB2004}.}
   \begin{tabular}{ccccc}
      \toprule
        & Units & Monthly Average & Weekly Average & Daily Maximum \\
      \midrule
      BOD$_5$           & mg/L      & 30                  & 45 & 60   \\
      Suspended Solids  & mg/L      & 30                  & 45 & 60   \\
      Settleable Solids & mL/L      & 0.1                 & -  & 0.2  \\
      Fecal Coliform    & MPN/100mL & 23                  & -  & 230   \\
      pH                & Standard  & $>$ 6.0 and $<$ 9.0 &    &      \\
      \bottomrule
   \end{tabular}\label{tab:002}
\end{table}

The AWWTF is responsible for reporting any permit violations to the
NCRWQCB, as well as providing monthly and annual self-monitoring
reports. From June of 2004 to March of 2007, the AWWTF accrued more
than \$54,000 in fines for 21 effluent violations, and \$216,600 in
fines for 17 sanitary sewer overflows. A complete list of discharge
permit violations is located in Appendix C.

\subsection{A Vision for the Brackish Marsh}
The construction of the 35 acre Brackish Marsh is part of a larger
McDaniel Slough restoration project. The project is funded and
managed by the Department of Fish and Game (DFG), in conjunction
with the City of Arcata. The Brackish Marsh is located directly
north of Gearheart Marsh, the second enhancement wetland (Appendix
B). The primary purpose of the Brackish Marsh is to provide a
specialized wildlife habitat containing a mixture of saltwater and
freshwater inputs. Saltwater is supplied by the tidal cycle through
a muted tide gate manufactured by Nehalem Marine Mfg. Freshwater
flow will be supplied from treated wastewater effluent in a
manneryet to be determined. The Brackish Marsh is designed to
receive 1 to 6 cfs in addition to 20 acres of upland surface runoff
\citep{CDFG2006}. A number of scenarios exist for the integration of
the Brackish Marsh into the existing treatment system, all of which
depend on the location of the new waste discharge permit
\citep{Andre2008}.

Multiple stakeholders of the Brackish Marsh Project (the City of
Arcata and the DFG) have conflicting ideals for the outcome of the
project. The DFG considers the Brackish Marsh as an extension of the
McDaniel Slough Project, while the City of Arcata and the AWWTF see
the Brackish Marsh as a source of increased wastewater treatment to
avoid discharge permit violations \citep{CDFG2006}.

\subsection{Description of Possible Alternatives - Proposed
Hydraulic Regimes} The exact integration of the Brackish Marsh into
the existing wastewater treatment system is still unknown, and
depends greatly on the location of the new waste discharge permit.
The North Coast Regional Water Quality Control Board's (NCRWQCB)
main objective for the McDaniel Slough Project is the restoration of
the designated project area, not necessarily the primary concern of
treatment plant operators. The NCRWQCB would like to designate the
enhancement marshes as "Waters of the U.S.", effectively removing
them from any effluent flow prior to the legal point of discharge.
The impact of such a decision could produce two major problems: (1)
a decrease in the ability of the treatment train to buffer extreme
flow events, and (2) increased fines due to mass and concentration
effluent violations. After consultation with the City of Arcata
Environmental Services Department, several hydraulic regimes were
outlined as possibilities for implementation \citep{Andre2008}. Each
possibility covers a different range of compromise between the
Arcata ESD and the North Coast Regional Water Quality Control Board
(NCRWQCB).

The first possibility is the addition of the Brackish Marsh to the
outfall of Hauser marsh. The waste discharge permit would be located
at the outfall of the Brackish Marsh tide gate (Figure
\ref{fig:option1}).
\begin{figure}[!h]
\centering \scalebox{0.6}{\includegraphics{figs/Option1.pdf}}
\caption{Flow diagram illustrating the full use of the enhancement
marshes.} \label{fig:option1}
\end{figure}
Full use of the enhancement marshes is ideal for several reasons.
The detention time provided by all three enhancement marshes results
in exceptional nutrient and mass removal, and provides a buffer for
extreme wastewater flow events. Although the enhancement marshes are
not currently operated in a variable manner, (ie. the water surface
elevations change only as a function of wastewater flow) the marshes
still provide the opportunity for operational flexibility. A
variation of the scenario presented in Figure \ref{fig:option1}
would split the flow exiting Hauser marsh into two streams.
Approximately 50\% of the effluent would return to the chlorine
contact basin before discharging into Butcher Slough or returning to
the enhancement wetlands, and the other 50\% would be discharged to
the Brackish Marsh.


The NCRWQCB would like to claim the enhancement marshes as "Waters
of the State," effectively removing them from the treatment train,
and placing the location of the discharge permit directly after the
contact basin (Figure \ref{fig:option5}).
\begin{figure}[!h]
\centering \scalebox{0.6}{\includegraphics{figs/Option5.pdf}}
\caption{Flow diagram illustrating the full removal of the
enhancement marshes.} \label{fig:option5}
\end{figure}
If implemented, the scenario in Figure \ref{fig:option5} would
significantly reduce the capacity of the treatment facility, as well
as the ability to successfully respond to extreme flow events. With
the enhancement marshes removed from the treatment train, the City
of Arcata is at a much higher risk of fines resulting from effluent
discharge violations.

The new discharge permit negotiations may also result in a partial removal of the enhancement marshes.
Partial removal would provide new water bodies for the NCRWQCB, and still provide a portion of the
original treatment and buffering capacity for the WWTF (Figure \ref{fig:option34}).
\begin{figure}[!h]
  \centering
     \subfigure[Diagram of flow through Allen and Gearheart Marshes.]{\includegraphics[scale=.3]{figs/Option3.pdf}}
     \centering
     \subfigure[Diagram of flow through Allen Marsh.]{\includegraphics[scale=.3]{figs/Option4.pdf}}
  \caption{Flow regime possibilities under the new permit of waste discharge.}
  \label{fig:option34}
\end{figure}

Possible modifications on the secondary treatment system will turn
oxidation pond 3 and the fish ponds into Treatment Marshes 4, 5, and
6 (Figure \ref{fig:NewTM}). Since the treatment marshes are a
limiting factor in the capacity and of the system, the addition of
three parallel treatment marshes will increase the treatment
capacity of the facility. The length to width ratios of the proposed
ponds are designed to provide optimal nutrient removal for the given
footprint. The addition of treatment marshes 4, 5, and 6 may produce
effluent of sufficient quality for direct chlorination and discharge
\citep{Gearheart2008}.
\begin{figure}[!h]
\centering\scalebox{0.6}{\includegraphics{figs/NewTM.pdf}}
\caption{Plan view of the proposed treatment marsh expansion and
associated modifications \citep{Burke2008}.} \label{fig:NewTM}
\end{figure}

\subsection{Treatment Plant Inflow Modeling}
Wastewater treatment plants are designed  using average flow values,
and average peak flows to provide adequate treatment without
over-designing the system. Treatment problems arise during the wet
season when precipitation causes the groundwater table to rise,
allowing water to infiltrate into the sewer collection system.
Infiltration is a result of leaky sewer collection systems and
illegal lateral connections, resulting in a high correlation between
precipitation and plant inflow. Inflow prediction based on
precipitation is vital for quantifying wastewater inflow and
enabling the operators to enforce corrective measures to ensure
compliance with the discharge permit.

Several options exist for modeling treatment plant inflow from
precipitation data. Artificial Neural Networks (ANN's) have
successfully produced high correlation coefficients (~0.9)for plant
inflow predictions based on precipitation \citep{El-Din2002}. {\it
Coulibaly et al}., 2005, used a combination of a Nearest Neighbor
Model, an ANN, and the conceptual model HSAMI. Weighted averages
were used from each model output to produce an estimation for
treatment plant inflow. \cite{Cleveland1990}, presents a Seasonal
Trend Loess (STL) model for characterizing the correlation between
two data sets based on the decomposition of periodic, non-stationary
time series. The STL model was chosen because it is simple to use
and easy to understand relative to the other models. The STL model
is also capable of analyzing data sets with missing values, and can
handle any size window of periodicity \citep{Mcleod1999}.

\subsection{Hydraulic Wetland Models}
Two main categories exist for modeling hydraulic dynamics in wetland
systems: lumped and distributed flow. Both models have the
capability of performing hydraulic and nutrient calculations, but
the analyses of this project are only concerned with hydraulics.

Distributed flow models use mass and momentum conservation equations
to determine flow patterns through ponds and/or wetlands. The
advantage of a distributed flow model is the ability to incorporate
short circuiting and dead zones, two common phenomena found in pond
and wetland systems that make modeling difficult. Common forms of
the distributed flow model are Manning's (open channel flow)
equation and the diffusion equation (flow through porous media). The
USGS groundwater model, MODFLOW, has a WETLANDS package that is
capable of simulating surface/groundwater interactions using a
distributed flow model, although the simultaneous solution is
computationally intensive \citep{Montoya1998}. MIKE-SHE is another
distributed flow model that is capable of modeling flow through
wetlands, ground/surface water interaction, and man made control
structures \citep{Thompson2004}. PHIM, a distributed flow model
based on a modified Manning's equation, was used to model wetlands
in the Great Lakes region to within one standard deviation of
observed values \citep{Guertin1987}.

Lumped flow models are large scale models that focus on the net
movement of water through a water body using mass conservation only.
Lumped models are preferable because they are less computationally
intensive, easier to solve, and perform better when physical data is
limited. Reservoir models are particular types of lumped models that
discretize the system area into a series of interconnected
reservoirs. A popular lumped flow models is the Army Corps of
Engineers' HEC-RAS model. Although primarily designed for modeling
river systems, \cite{HEC2008} proposed the use of HEC-RAS for
modeling wetlands predominated by sloughs and vegetated channels.
PondPack is a linear reservoir model capable of simulating control
structures such as weirs and tide gates, and accounts for hydrologic
considerations like precipitation and evaporation
\citep{Haestad2005}.


\subsection{Tide Gates}
Tide gates are hydraulic control structures that prevent the back
flow of saltwater into estuaries or marshes. Historically, tide
gates have been installed in dike structures in order to drain
marshes and estuaries in preparation for land use purposes
\citep{Giannico2005}. Tide gates utilize one directional single or
double hinged flaps at the downstream (saltwater) side of a dike
culvert. The one directional hinges only allow the transfer of water
into the saltwater body based on a head differential. As the tide
rises, the gate remains closed, keeping water from flowing upstream
into the marsh or estuary. During low tides when the head level on
the upstream side of the culvert is greater than the downstream
side, the gate opens allowing the downstream flow of water. Improper
selection of tide gate invert elevations can cause malfunctioning,
especially if placed too high at the freshwater/saltwater interface.
If the gate is placed too high, the flap may fail to open during low
tides due to a minimal or non-existent head difference between the
two water bodies \citep{Giannico2005}. Some tide gates are
manufactured with pet doors to allow for fish passage and brackish
conditions on the upstream side.

\subsubsection{Types of Tide Gates}
Tide gates are typically top or side hinged devices made of wood,
cast iron, or aluminum. Side hinged gates require less head
differential to open and provide greater opportunity for fish
passage \citep{Giannico2005}. Since the gate will still block fish
passage by closing for most of the tidal cycle, pet doors have been
introduced into some designs to facilitate fish passage throughout
the tidal cycle. For the McDaniel Slough restoration project,
Nehalim Marine has developed a tide gate with a pet door, termed a
Muted Tidal Regulator (MTR), to allow for fish passage while
preventing saltwater back flow \citep{Kuntz2008}. The operation of
the pet door is regulated by a buoy on the upstream side. When water
levels on the upstream side are low, the pet door remains open. As
the upstream water level increases, the buoy is raised, and the pet
door closes. During times of high tide and low upstream water
levels, the tide gate will be closed, but the pet door will be open,
allowing the upstream flow of saltwater. When both the tide and
upstream water levels are high, the pet door will remain closed, and
the main gate will open and close based on the head differential
\citep{Kuntz2008}. The MTR allows for the upstream flow of saltwater
to create the desired conditions for the Brackish Marsh.

\subsubsection{Modeling Tide Gates}
Tide gate modeling with the inclusion of a pet door is presented by
\cite{Porior2003}. Two scenarios were analyzed to determine flow
velocities for upstream fish passage viability: (1) the pet door is
fully open and flowrates calculated using a frictional head loss
equation, and (2) the pet door is partially open and flowrates
calculated using a weir equation.

\cite{Litrico2005} presented a hydraulic model for operating a
Begemann automated tide gate. A Begemann gate consists of a round
gate that rotates around a horizontal axis in response to head
differentials. Modeling was conducted by finding the moment of the
gate, and assuming hydrostatic conditions nad negligible friction
losses when the gate is open. The angle of the gate opening governs
the equation used to calculate flow. When the angle of the gate
opening is small, the gate is modeled as an orifice. When the angle
of the gate opening is large, the gate is modeled with a weir
equation.

The modeling of Vlugter gates, a modified version of a Begemann gate
was presented by \cite{Belaud2008}. The gate is designed to operate
under submerged conditions by allowing water to flow under and
around the gate. Flow under the gate was modeled as flow through an
orifice, while flow around the gate was modeled as flow over a weir.

\subsection{Data Sources}
Implementation of the hydraulic model outlined in Section 4 requires
the input of certain spatial characteristics of the wastewater
treatment system. The hydraulic model must be based on absolute
elevations in order to be properly integrated with NOAA's ADCIRC
model. Elevation data for the tops of weir and sluice boxes for all
treatment pond, treatment marsh, and enhancement marsh inlets and
outlets were compiled from a survey conducted in the summer of 2008
\citep{COA2008}. Absolute weir and sluice crest elevations were
calculated from collected field measurements and consultation of the
treatment facility plans \citep{CH2MHill}. Spatial analyses of all
ponds and marshes was conducted using GIS data layers provided by
the City of Arcata \citep{Kang2008}.

The flow of wastewater through the treatment ponds and wetlands is
constrained by the plumbing system and pumping capacities, and the
configuration of weirs/sluice gates. Although the plant is generally
operated with minimal hydraulic variation, extreme inflow cases do
require alteration of the system in order to protect against
discharge violations, infrastructure damage, and dike overtopping
\citep{Clinton2008}. All possible flow routes through the treatment
ponds, marshes, and enhancement wetlands are diagramed in Appendix
A.

Predicting wastewater inflow requires the concurrent analysis of
treatment plant inflow data and precipitation data. Three
precipitation data sets are available for analysis: one stationed at
the NOAA weather station on Woodley Island near Eureka, one
stationed at the Redwood Sciences Laboratory in the Arcata Community
Forest, and one stationed at a residence in Sunny Brae
\citep{Ruegg2008}. All data sets provided adequate time series
duration for proper analysis and correlation. The Woodley Island
data set was chosen because precipitation data is continuously
updated to the NOAA database and made available for download,
whereas the other two data sets must be manually collected and
updated. Only one data set of daily wastewater flows was available
for the AWWTF inflow analysis \citep{Finney2008}.

\section{Methodology}
\subsection{STL Inflow Modeling}
The modeling of treatment plant inflow is conducted with the STL
procedure. The procedure is based on the decomposition of each data
set into three parts: a seasonal component (s), a trend component
(t), and a remainder component ($r$). The seasonal and trend
portions are determined and subtracted from each data set, leaving a
remainder value for each data point. The data sets are then
correlated using the remainder values. At this point, the
relationship between remainder values of each data set is assumed
linear and can be determined from a linear regression as follows:
\begin{equation}
r_{inflow}=a+br_{precip}
\end{equation}
where $a$ and $b$ are parameters of the linear regression model.
Once the remainder values for the plant inflow data are determined,
the seasonal and trend portions are added back onto the remainder,
and an inflow value is obtained. The STL procedure also accounts for
the compounding nature of consecutive days of precipitation. The
idea is that the previous $m$ days of precipitation have a stronger
correlation with plant inflows than any single day single day due to
the time lag and storage associated with groundwater flow.

\subsection{Pond and Wetland Modeling}
The hydraulic behavior of the treatment system is modeled via a
linear reservoir model. Use of the linear reservoir model requires
three main assumptions: (1) the water surface elevation across a
given reservoir is uniform, (2) the stage-discharge relationship
remains unchanged between the filling and emptying stages, and (3)
the water surface elevation of the reservoir remains constant during
a given time-step, therefore the flowrate is constant over the same
time-step. We have also assumed that the surface area of each
reservoir remains constant as the water surface elevation
fluctuates. The mass conservation expression used to describe flow
through the reservoir is:
\begin{equation}
A\frac{\Delta H}{\Delta t}=Q_{in}-Q_{out}(H)
\end{equation}
where $A$ is the reservoir surface area, $H$ is the water surface
elevation, $Q_{in}$ is the flowrate into the reservoir, $Q_{out}(H)$
is the stage discharge relationship (a function of the outlet
structure), and $t$ is time. Some of the most widely accepted weir
equations were presented by \cite{King1963}, for flow over submerged
and non-submerged weirs. The approach velocities for both types of
weir configurations are considered negligible. \cite{King1963}, also
present equations for computing head loss through pipes and gates
under turbulent flow conditions.


Calculation of flowrates from one reservoir to another requires that
head losses due to friction are known. In order to compute head
losses and flowrates through control structures similar to that in
Figure \ref{fig:prototype}, an iterative process outlined by
\cite{Chow1988} is utilized (Figure \ref{fig:flowchart}).
\begin{figure}[!h]
\centering\scalebox{2.3}{\includegraphics{figs/prototype.pdf}}
\caption{A prototypical control structure with labeled parameters.}
\label{fig:prototype}
\end{figure}
\begin{figure}[!h]
\centering\scalebox{0.4}{\includegraphics{figs/flowchart.pdf}}
\caption{A conceptual simulation process diagram.}
\label{fig:flowchart}
\end{figure}
Flowrates are estimated without frictional losses. The computed
flowrate is then used to calculate the head loss across the control
structure. Flowrates are then re-computed with the estimated head
loss taken into account. Once the flowrates between iteration $i$
and $i-1$ are equal, a third order Runge-Kutta routine is used to
calculate the resulting conditions for a given timestep
\citep{Chow1988}. Since the weir elevations are seldom adjusted in
practice, the corresponding weir parameters remain unchanged
throughout a simulation. All timesteps of the model are computed,
and the change in water surface elevations in each reservoir is
determined for the entire duration of the simulation.

\clearpage
%looks for the bibtex file refs.bib
\addcontentsline{toc}{section}{References}
\bibliography{references}

\newpage
\addcontentsline{toc}{section}{Appendix A}
{\Large{\bf Appendix A:}} Diagram of the AWWTF \citep{Reiss1996}.\\
\scalebox{.244}{\rotatebox{90}{\includegraphics{figs/marsh.pdf}}}
\newpage
\addcontentsline{toc}{section}{Appendix B}
{\Large{\bf Appendix B:}}
The proposed McDaniel Slough restoration
project area \citep{CDFG2006}.\\
\scalebox{.89}{\includegraphics{figs/McDaniel_Slough.pdf}}
\newpage
\addcontentsline{toc}{section}{Appendix C}
{\Large{\bf Appendix C:}} Effluent discharge violations from 2004 to 2007 \citep{CRWQCB2004}. \\
\begin{center}
\scalebox{.8}{\includegraphics{figs/Violation_List_1.pdf}}\\
\newpage
\scalebox{.8}{\includegraphics{figs/Violation_List_2.pdf}}
\end{center}

\end{document}
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